I just updated the Steam version of the game to the newest patch. I tried to log in three times (twice with normal account info, once with the Login Through Steam button), and all three times my mouse cursor turned into a beach ball and nothing happened. Checking the taskbar showed that the application was not responding.
Edit: Trying to log in through my phone had a similar effect, nothing happened when I pressed the log in button, until the app closed itself. A second attempt at this lead to a server maintenance message, long after pressing the log in button